A121064 Number of length-n American English expressions for nonnegative integers (spaces, hyphens, and commas excluded).

0, 0, 0, 4, 4, 6, 6, 3, 13, 22, 35, 32, 36, 89, 158, 342, 586, 913, 1490, 2365, 3884, 5940, 8629, 12386, 17637, 26311

Offset

0,4

Comments

These are Mathematica integer names (using qualifier "Words") < 10^306.

References

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 123, Problem 6.

Links

Table of n, a(n) for n=0..25.

Hans Havermann, A dictionary of American English integer names (by letter count, to 13 letters).

Hans Havermann, 14- to 40-letter integer names.

Formula

a(n) = # {m | A005589(m)=n }. - M. F. Hasler, Sep 07 2012

Example

a(3) = 4 since there are only 4 numbers in English with 3 letters: one, two, six, ten.
a(4) = 4 since there are only 4 numbers in English with 4 letters: zero, four, five, nine.
a(10) = 35 (24, 25, 29, 34, 35, 39, 43, 47, 48, 53, 57, 58, 63, 67, 68, 71, 72, 76, 84, 85, 89, 94, 95, 99, 100, 200, 600, 1000000, 2000000, 6000000, 10000000, 1000000000, 2000000000, 6000000000, 10000000000)
a(11) = 32:  [2389][378],7[459], [459]00, [126]000, 10000, [459]000000, [459]000000000, [126]000000000000, 10 trillion.

Crossrefs

Cf. A052193, A362449.

Sequence in context: A332917 A016710 A225134 * A213342 A019559 A365198

Adjacent sequences: A121061 A121062 A121063 * A121065 A121066 A121067

Keyword

more,nonn,word,fini

Author

Ray G. Opao, Aug 10 2006

Extensions

Corrected and extended by Hans Havermann, Sep 08 2012

Recorrected (using a larger number limit) by Hans Havermann, Apr 23 2023

Status

approved